Multiway p-spectral graph cuts on Grassmann manifolds

Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering algorithm in the p-norm, for $$p\in (1,2]$$ p ∈ ( 1 , 2 ] . The problem of computing multiple eigenvectors of the graph p-Laplacian, a nonlinear generalization of the standard graph Laplacian, is recasted as an unconstrained minimization problem on a Grassmann manifold. The value of p is reduced in a pseudocontinuous manner, promoting sparser solution vectors that correspond to optimal graph cuts as p approaches one. Monitoring the monotonic decrease of the balanced graph cuts guarantees that we obtain the best available solution from the p-levels considered. We demonstrate the effectiveness and accuracy of our algorithm in various artificial test-cases. Our numerical examples and comparative results with various state-of-the-art clustering methods indicate that the proposed method obtains high quality clusters both in terms of balanced graph cut metrics and in terms of the accuracy of the labelling assignment. Furthermore, we conduct studies for the classification of facial images and handwritten characters to demonstrate the applicability in real-world datasets.

The Larger the Better: Analysis of a Scalable Spectral Clustering Algorithm with Cosine Similarity

Chen (2018) proposed a scalable spectral clustering algorithm for cosine similarity to handle the task of clustering large data sets. It runs extremely fast, with a linear complexity in the size of the data, and achieves state of the art accuracy. This paper conducts perturbation analysis of the algorithm to understand the effect of discarding a perturbation term in an eigendecomposition step. Our results show that the accuracy of the approximation by the scalable algorithm depends on the connectivity of the clusters, their separation and sizes, and is especially accurate for large data sets.

Power System Zone Partitioning Based on Transmission Congestion Identification Using an Improved Spectral Clustering Algorithm

The ever-expanding power system is developed into an interconnected pattern of power grids. Zone partitioning is an essential technique for the operation and management of such an interconnected power system. Owing to the transmission capacity limitation, transmission congestion may occur with a regional influence on power system. If transmission congestion is considered when the system is decomposed into several regions, the power consumption structure can be optimized and power system planning can be more reasonable. At the same time, power resources can be properly allocated and system safety can be improved. In this paper, we propose a power system zone partitioning method where the potential congested branches are identified and the spectral clustering algorithm is improved. We transform the zone partitioning problem into a graph segmentation problem by constructing an undirected weighted graph of power system where the similarities between buses are measured by the power transfer distribution factor (PTDF) corresponding to the potential congested branches. Zone partitioning results show that the locational marginal price (LMP) in the same zone is similar, which can represent regional price signals and provide regional auxiliary decisions.

Audit Analysis of Abnormal Behavior of Social Security Fund Based on Adaptive Spectral Clustering Algorithm

Abnormal behavior detection of social security funds is a method to analyze large-scale data and find abnormal behavior. Although many methods based on spectral clustering have achieved many good results in the practical application of clustering, the research on the spectral clustering algorithm is still in the early stage of development. Many existing algorithms are very sensitive to clustering parameters, especially scale parameters, and need to manually input the number of clustering. Therefore, a density-sensitive similarity measure is introduced in this paper, which is obtained by introducing new parameters to transform the Gaussian function. Under this metric, the distance between data points belonging to different classes will be effectively amplified, while the distance between data points belonging to the same class will be reduced, and finally, the distribution of data will be effectively clustered. At the same time, the idea of Eigen gap is introduced into the spectral clustering algorithm, and the verified gap sequence is constructed on the basis of Laplace matrix, so as to solve the problem of the number of initial clustering. The strong global search ability of artificial bee colony algorithm is used to make up for the shortcoming of spectral clustering algorithm that is easy to fall into local optimal. The experimental results show that the adaptive spectral clustering algorithm can better identify the initial clustering center, perform more effective clustering, and detect abnormal behavior more accurately.

An Enhanced Spectral Clustering Algorithm with S-Distance

Calculating and monitoring customer churn metrics is important for companies to retain customers and earn more profit in business. In this study, a churn prediction framework is developed by modified spectral clustering (SC). However, the similarity measure plays an imperative role in clustering for predicting churn with better accuracy by analyzing industrial data. The linear Euclidean distance in the traditional SC is replaced by the non-linear S-distance (Sd). The Sd is deduced from the concept of S-divergence (SD). Several characteristics of Sd are discussed in this work. Assays are conducted to endorse the proposed clustering algorithm on four synthetics, eight UCI, two industrial databases and one telecommunications database related to customer churn. Three existing clustering algorithms—k-means, density-based spatial clustering of applications with noise and conventional SC—are also implemented on the above-mentioned 15 databases. The empirical outcomes show that the proposed clustering algorithm beats three existing clustering algorithms in terms of its Jaccard index, f-score, recall, precision and accuracy. Finally, we also test the significance of the clustering results by the Wilcoxon’s signed-rank test, Wilcoxon’s rank-sum test, and sign tests. The relative study shows that the outcomes of the proposed algorithm are interesting, especially in the case of clusters of arbitrary shape.